Intermolecular Potential and Lattice Dynamics of the CO2 Crystal

Abstract

The lattice dynamics of solid CO₂ has been treated throughout the Brillouin zone. The molecular librational degrees of freedom have been treated by the use of Eulerian displacement coordinates. The potential model assumes the molecule represented by two centers of interaction (diatomic model) and each molecular pair interaction term is written as a sum of 6–12 terms between interaction centers on different molecules. The three parameters of the potential are obtained by fitting to the five optic modes, from the crystal energy, and by invoking the condition of zero uniform stress. It is found that the interaction between translational and librational degrees of freedom is large inside the Brillouin zone. The low temperature specific heat was calculated and found to agree well with experimental data. In an appendix, the applicability of the classical harmonic oscillator treatment to small molecular solids is discussed, and it is concluded that this approach is justified for solid CO₂.